limit

Re: limit

I would say it is either 1 or non-existent...

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: limit

hi mitu, I would say it does not exist if your succession is from N to R; here's a short proof of non-existence:if LIM[a(n)]=L, then for all a(n(k)) LIM[a(n(k))]=Lyou see that LIM[a(2k)]!=L since a(2k) is not defined for each k. But maybe someone would argue that for each n in dom(a(n)) a(n)=-1, so LIMa(n)=-1... i see it just as a formal problem, maybe someone can be more precise.

While writing my post i realized that if your succession is from N to C it is not even a function, so i don't know if it has any meaning to talk about limit...

Re: limit

What do you mean by a succession from N to C?

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: limit

I have to admit that at first sight this looked funny; but after being (maybe) less superficial i'm seeing a meaning behind this:look it geometrically (i write polar coordinates for complex numbers)...

Re: limit

Hi!

I assume that we are dealing with the PRINCIPAL roots of -1 (when k=0) since for each n there are ndistinct roots of -1 equally spaced about the unit circle. Fistfiz's example using the clock gives a goodillustration of that sequence progressing counterclockwise from e^ipi to 1 around the top of the circle.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).LaTex is like painting on many strips of paper and then stacking them to see what picture they make.